{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7.4.1 梯度下降的问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "让我们考虑一个输入和输出分别为二维向量$\\boldsymbol{x} = [x_1, x_2]^\\top$和标量的目标函数$f(\\boldsymbol{x})=0.1x_1^2+2x_2^2$。与7.2节中不同，这里将$x_1^2$系数从$1$减小到了$0.1$。下面实现基于这个目标函数的梯度下降，并演示使用学习率为$0.4$时自变量的迭代轨迹。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.943467, x2 -0.000073\n"
     ]
    },
    {
     "data": {
      "image/png": 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a+P3Ny7hkbSO+uYpI+1ZjMYKCqjZo31aWX0kQBAFEOOaPSd7h8NsWV2xs4YqN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\nZmZWihuHmZmV4sZhZmal/An3uFS2CydpLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e43ff5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import time\n",
    "import sys\n",
    "import tensorflow as tf\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_tensorflow2 as d2l\n",
    "\n",
    "eta = 0.4 # 学习率\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.387814, x2 -1673.365109\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ap937/2XPBL4DtAA3hzeAbwNXm9kmYAfB0WYiItXTSZSJ1SRc3P1a4NoKz10E\nXFSmfT2wqEx7F3By2n0UEVFBP7l6mxYTEakfKugnpnAREalEBf3EFC4iIpWooJ+YwkVEpBIV9BNT\nuIiIVKJVkRNTuIiIVJJRuCSlcBERqUQF/cQULiIilWhV5MQULiIilaign5jCRUSkEsvqJMqEFC4i\nIpWo5pKYwkVEpBKFS2IKFxGRSlTQT0zhIiJSiVZFTkzhIiJSiVZFTkzhIiJSiWouiSlcREQqUbgk\npnAREalEBf3EFC4iIpVoVeTEFC4iIpVoVeTEFC4iIpVobbHEFC4iIpXoMseJKVxERCqJRi7ute7J\nuKNwERGpxLLBvetEypFSuIiIVJIJw0VF/RGrSbiY2clmttHMCma2JNY+38z2mtn94e0/Ys8dbWYP\nmNkmM1tjZha2N5vZNWH7XWY2f+z3SEQaUn+4qKg/UrUauTwIfAC4o8xzT7j7UeHtk7H2y4AzgIXh\nbVnYfjqw090PA1YDXx+9bovIhJLJBfcq6o9YTcLF3R9290eH+3ozmw1Mc/c73d2Bq4CTwqeXA1eG\n2z8GlkajGhGRqkThopHLiNVjzWVBOCX2KzP707BtDrA19pqtYVv03BYAd+8DOoAZY9VZEWlgpppL\nUrnR+mAzux04uMxT57r7dRXe9hwwz923m9nRwH+b2REp9mklsBJg3rx5aX2siDQqFfQTG7Vwcfd3\nJ3hPN9Adbt9rZk8AfwRsA+bGXjo3bCO8bwe2mlkOaAO2V/j8y4HLAZYsWaID10VkaCroJ1ZX02Jm\nNtMsGIea2aEEhfsn3f05oNPM3hLWUz4GRKOf64HTwu0PAT8P6zIiItVRQT+xWh2K/H4z2wq8Ffip\nmd0SPvV2YIOZ3U9QnP+ku+8InzsT+E9gE/AEcHPY/m1ghpltAj4HnD1GuyEijc40cklq1KbFhuLu\n1wLXlmn/CfCTCu9ZDywq094FnJx2H0VEikeL6Qz9kaqraTERkbqimktiChcRkUoULokpXEREKlFB\nPzGFi4hIJSroJ6ZwERGp5OnfBvffWgqrF8GGtbXtzziicBERKWfDWrgrWpjdoWML3LBKATNMChcR\nkXLWXQD57oFtvXuDdtknhYuISDkdW0fWLgMoXEREymmbO7J2GUDhIiJSztLzoKllYFtTS9Au+6Rw\nEREpZ/EKOHENtLUDFtyfuCZol32qydpiIiLjwuIVCpOENHIREZHUKVxERCR1ChcREUmdwkVERFKn\ncBERkdS5Sb4ZAAAD3klEQVTZRL3cvJm9BDw9Bj/qQODlMfg5Y6nR9kn7U98abX9gfO/Ta9x95r5e\nNGHDZayY2Xp3X1LrfqSp0fZJ+1PfGm1/oDH3qZSmxUREJHUKFxERSZ3CZfRdXusOjIJG2yftT31r\ntP2BxtynAVRzERGR1GnkIiIiqVO4jAEzO9/MtpnZ/eHtL2rdpzSY2efNzM3swFr3pVpmdqGZbQj/\nfW41s0Nq3adqmNnFZvZIuE/Xmtn+te5TNczsZDPbaGYFMxu3R1mZ2TIze9TMNpnZ2bXuz2hSuIyd\n1e5+VHi7qdadqZaZtQPHA8/Uui8pudjdF7v7UcCNwHi/aMdtwCJ3Xww8BpxT4/5U60HgA8Adte5I\nUmaWBS4B/hw4HDjVzA6vba9Gj8JFkloNfBFoiKKdu3fGHk5lnO+Xu9/q7n3hwzuBcX35RHd/2N0f\nrXU/qnQMsMndn3T3HuCHwPIa92nUKFzGzmfDKYorzOyAWnemGma2HNjm7n+odV/SZGYXmdkW4COM\n/5FL3N8AN9e6E8IcYEvs8dawrSHpYmEpMbPbgYPLPHUucBlwIcFfwxcC3yT4H75u7WN/vkQwJTau\nDLVP7n6du58LnGtm5wCfAf5+TDs4Qvvan/A15wJ9wPfGsm9JDGd/ZPxQuKTE3d89nNeZ2bcI5vTr\nWqX9MbMjgQXAH8wMgumW35vZMe7+/Bh2ccSG+29E8EV8E3UeLvvaHzP7K+C9wFIfB+ccjODfZ7za\nBrTHHs8N2xqSpsXGgJnNjj18P0Fxclxy9wfcfZa7z3f3+QRD+z+u92DZFzNbGHu4HHikVn1Jg5kt\nI6iJvc/dX611fwSAe4CFZrbAzCYBpwDX17hPo0Yjl7HxDTM7imBa7CngE7XtjpTxNTN7HVAgWC37\nkzXuT7X+HWgGbgtHmHe6+7jdJzN7P/BvwEzgp2Z2v7ufUONujYi795nZZ4BbgCxwhbtvrHG3Ro3O\n0BcRkdRpWkxERFKncBERkdQpXEREJHUKFxERSZ3CRUREUqdwEalDZvYzM9tlZnV/wq1IOQoXkfp0\nMfDRWndCJCmFi0gNmdmbwwVNJ5vZ1PCaJYvcfR2wu9b9E0lKZ+iL1JC732Nm1wP/CLQA33X3cbs8\nkEhE4SJSexcQrDvVBayqcV9EUqFpMZHamwG0AvsBk2vcF5FUKFxEau//Al8hWOr/6zXui0gqNC0m\nUkNm9jGg192/H15j/bdm9i7gH4DXA61mthU43d1vqWVfRUZCqyKLiEjqNC0mIiKpU7iIiEjqFC4i\nIpI6hYuIiKRO4SIiIqlTuIiISOoULiIikjqFi4iIpO7/Ax6qKuyyiYGlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e5693fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.6\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4.2 动量法\n",
    "\n",
    "动量法的提出是为了解决梯度下降的上述问题。由于小批量随机梯度下降比梯度下降更为广义，本章后续讨论将沿用7.3节（小批量随机梯度下降）中时间步$t$的小批量随机梯度$\\boldsymbol{g}_t$的定义。设时间步$t$的自变量为$\\boldsymbol{x}_t$，学习率为$\\eta_t$。\n",
    "在时间步$0$，动量法创建速度变量$\\boldsymbol{v}_0$，并将其元素初始化成0。在时间步$t>0$，动量法对每次迭代的步骤做如下修改：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\boldsymbol{v}_t &\\leftarrow \\gamma \\boldsymbol{v}_{t-1} + \\eta_t \\boldsymbol{g}_t, \\\\\n",
    "\\boldsymbol{x}_t &\\leftarrow \\boldsymbol{x}_{t-1} - \\boldsymbol{v}_t,\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.062843, x2 0.001202\n"
     ]
    },
    {
     "data": {
      "image/png": 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zgLwpMlLKFqtsF0LcA6wH8gqH1RvZCGqOY6ztPxQnLq7kxMWVtPRE+OWmJn6z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\nmlHhNA1qSjzUjCDqFbLDZoGwEpnenBS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      "text/plain": [
       "<matplotlib.figure.Figure at 0xf2a9e7cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def momentum_2d(x1, x2, v1, v2):\n",
    "    v1 = gamma * v1 + eta * 0.2 * x1\n",
    "    v2 = gamma * v2 + eta * 4 * x2\n",
    "    return x1 - v1, x2 - v2, v1, v2\n",
    "\n",
    "eta, gamma = 0.4, 0.5\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4.3 从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features, labels = d2l.get_data_ch7()\n",
    "\n",
    "def init_momentum_states():\n",
    "    v_w = tf.zeros((features.shape[1],1))\n",
    "    v_b = tf.zeros(1)\n",
    "    return (v_w, v_b)\n",
    "def sgd_momentum(params, states, hyperparams,grads):\n",
    "    i=0\n",
    "    for p,v in zip(params, states):\n",
    "        v=hyperparams['momentum'] * v + hyperparams['lr'] * grads[i]\n",
    "        p.assign_sub(v)\n",
    "        i+=1\n",
    "def init_momentum_states():\n",
    "    v_w = tf.zeros((features.shape[1],1))\n",
    "    v_b = tf.zeros(1)\n",
    "    return (v_w, v_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss: 0.245740, 1.004673 sec per epoch\n"
     ]
    },
    {
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   "source": [
    "d2l.train_ch7(sgd_momentum, init_momentum_states(),\n",
    "              {'lr': 0.004, 'momentum': 0.9}, features, labels)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7.4.4. 简洁实现¶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from tensorflow.keras import optimizers\n",
    "trainer = optimizers.SGD(learning_rate=0.004,momentum=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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     "text": [
      "loss: 0.515107, 1.313495 sec per epoch\n"
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